Surface height recovery using heat flow and manifold embedding

This paper describes a graph-spectral method for shape-from-shading. The algorithm takes as its input a field of initial surface normal estimates computed using the Lambertian irradiance cone and the Canny edge gradient. We illustrate how to refine this field of surface normals using a graph-spectral method. From the initial field of surface normals we make curvature estimates. The curvature estimates are in turn used to compute a transition probability matrix. From the theory of random walks on graphs, the leading eigenvector of this matrix is a curvature minimising path through the field of surface normals. We impose curvature consistency on the initially noisy field of surface normals by rotating them about their irradiance cones so that they follow the path defined by the leading eigenvector. This method is applied to a variety of real-world images and is shown to lead to improved surface reconstruction.

In this paper we explore the use of complex numbers as means of representing angular statistics for surface normal data. Our aim is to use the representation to construct a statistical model that can be used to describe the variations in fields of surface normals. We focus on the problem of representing facial shape. The fields of surface normals used to train the model are furnished by range images. We compare the complex representation with one based on angles, and demonstrate the advantages of the new method. Once trained, we illustrate how the model can be fitted to brightness images by searching for the set of parameters that both satisfy Lambert’s law and minimize the integrability error.KeywordsZenith AngleAzimuth AngleRange ImageIntegrability ErrorStatistical Shape ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents an empirical study to investigate the use of photometric stereo (PS) for micro-scale 3D measurement of paper samples. PS estimates per-pixel surface orientation from images of a surface captured from the same viewpoint but under different illumination directions. Specifically, we investigate the surface properties of paper to test whether they are sufficiently well approximated by a Lambertian reflectance model to allow veridical surface reconstruction under PS and explore the range of conditions for which this model is valid. We present an empirical setup that is used to conduct a series of experiments in order to analyse the applicability of PS at the micro-scale. In addition, we determine the best 4, 6, and 8 light source tilt (illumination) angles with respect to multi-source micro-scale PS. Furthermore, an intensity based image registration method is used to test the accuracy of the recovery of surface normals. The results demonstrate that at the micro-scale: (a) Lambert model represents well the data sets with low root mean square (RMS) error between the original and reconstructed image, (b) increasing the light sources from 4 to 8 reduces RMS error, and (c) PS can be used to extract veridical surface normals.

Photometric stereo (PST) is a widely used technique of estimating surface normals from an image set. However, it often produces inaccurate results for non-Lambertian surface reflectance. In this study, PST is reformulated as a sparse recovery problem where non-Lambertian errors are explicitly identified and corrected. We show that such a problem can be accurately solved via a greedy algorithm called orthogonal matching pursuit (OMP). The performance of OMP is evaluated on synthesized and real-world datasets: we found that the greedy algorithm is overall more robust to non-Lambertian errors than other state-of-the-art sparse approaches with little loss of efficiency. Along with providing an overview of current methods, novel contributions in this paper are as follows: we propose an alternative sparse formulation for PST; in previous PST studies (Wu et al., Robust photometric stereo via low-rank matrix completion and recovery, 2010), (S. Ikehata et al., Robust photometric stereo using sparse regression, 2012), the surface normal vector and the error vector are treated as two entities and are solved independently. In this study, we convert their formulation into a new canonical form of the sparse recovery problem by combining the two vectors into one large vector in a new “stacked” formulation in this domain. This allows for a large repertoire of existing sparse recovery algorithms to be more straightforwardly applied to the PST problem. In our application of the OMP greedy algorithm, we show that greedy solvers can indeed be applied, with this study supplying the first of such attempt at employing greedy approaches to estimate surface normals within the framework of PST. We numerically compare the performance of several normal vector recovery methods. Most notably, this is the first detailed test on complex images of the normal estimation accuracy of our previously proposed method, least median of squares (LMS).

Three-dimensional reconstruction technologies are fundamental problems in computer vision. Photometric stereo recovers the surface normals of a 3D object from varying shading cues, prevailing in its capability for generating fine surface normal. In recent years, deep learning-based photometric stereo methods are capable of improving the surface-normal estimation under general non-Lambertian surfaces, due to its powerful fitting ability on the non-Lambertian surface. These state-of-the-art methods however usually regress the surface normal directly from the high-dimensional features, without exploring the embedded structural information. This results in the underutilization of the information available in the features. Therefore, in this paper, we propose an efficient manifold-based framework for learning-based photometric stereo, which can better map combined high-dimensional feature spaces to low-dimensional manifolds. Extensive experiments show that our method, learning with the low-dimensional manifolds, achieves more accurate surface-normal estimation, outperforming other state-of-the-art methods on the challenging DiLiGenT benchmark dataset.

This paper presents symmetric-light photometric stereo for surface normal estimation, in which directional lights are distributed symmetrically with respect to the optic center. Unlike previous studies of ring-light settings that required the information of ring radius, we show that even without the knowledge of the exact light source locations or their distances from the optic center, the symmetric configuration provides us sufficient information for recovering unique surface normals without ambiguity. Specifically, under the symmetric lights, measurements of a pair of scene points having distinct surface normals but the same albedo yield a system of constrained quadratic equations about the surface normal, which has a unique solution. Experiments demonstrate that the proposed method alleviates the need for geometric light source calibration while maintaining the accuracy of calibrated photometric stereo.

In this note I give an alternative proof of some of the properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, which Pleijel and I proved some time back [2]. Instead of using Carleman's method, I use the heat equation as I did in the case of the Euclidean space [1].

We consider the problem of estimating surface normals of a scene with spatially varying, general bidirectional reflectance distribution functions (BRDFs) observed by a static camera under varying distant illuminations. Unlike previous approaches that rely on continuous optimization of surface normals, we cast the problem as a discrete search problem over a set of finely discretized surface normals. In this setting, we show that the expensive processes can be precomputed in a scene-independent manner, resulting in accelerated inference. We discuss two variants of our discrete search photometric stereo (DSPS), one working with continuous linear combinations of BRDF bases and the other working with discrete BRDFs sampled from a BRDF space. Experiments show that DSPS has comparable accuracy to state-of-the-art exemplar-based photometric stereo methods while achieving 10-100x acceleration.

We address the problem of reconstructing 3D surfaces from depth and surface normal maps acquired by a sensor system based on a single perspective camera. Depth and normal maps can be obtained through techniques such as structured‐light scanning and photometric stereo, respectively. We propose a perspective‐aware log‐depth fusion approach that extends existing orthographic gradient‐based depth‐normals fusion methods by explicitly accounting for perspective projection, leading to metrically accurate 3D reconstructions. Additionally, the method handles missing depth measurements by leveraging available surface normal information to inpaint gaps. Experiments on the DiLiGenT‐MV data set demonstrate the effectiveness of our approach and highlight the importance of perspective‐aware depth‐normals fusion.

In the objective research field of traditional Chinese medicine (TCM) tongue diagnosis, 2D tongue image is regarded as the research object for feature extraction and analysis in most current methods. However, 2D tongue image always can not visually express detail information of tongue 3D surface, such as lingual papilla, prick and fissure of tongue. It brings certain limitations to perceive real tongue surface. It is limited for the doctor to give accurate diagnosis. To solve this problem, a method to reconstruct the 3D surface of tongue based on photometric stereo is proposed. First, the surface normals and texture reflectance are obtained using photometric stereo technology in this paper, then calculate the depth values of tongue surface, and generate 3D depth map. It has been proved that the method is viable through lots of experiments and doctors may observe the 3D information of tongue surface from multiple perspectives. Detail information of tongue surface also may be expressed quantitatively and visually.

We introduce a new approach for recovering shape-from-shading (SFS) from synthetic aperture radar (SAR) images of the terrain. Three contributions are proposed: 1) we show how the direction of surface normals is constrained by the geometry of the radar reflectivity cone; 2) we show how topographic features can be used as boundary constraints on the recovered surface normals; and 3) the resulting field of surface normals is smoothed using robust statistics.

The aim in this paper is to show how to discriminate gender using a parameterized representation of fields of facial surface normals (needle-maps) which can be extracted from 2D intensity images using shape-from-shading (SFS). We makes use of principle geodesic analysis (PGA) to parameterize the facial needle-maps. Using feature selection, we determine which of the components of the resulting parameter vector are the most significant in distinguishing gender. Using the EM algorithm we distinguish gender by fitting a two component mixture model to the vectors of selected features. Results on real-world data reveal that the method gives gender discrimination results that are comparable to human observers.KeywordsFeature SelectionMixture ModelGaussian Mixture ModelGender DiscriminationFeature ComponentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To investigate the validity of appending the Gorter-Mellink friction term to the equations of motion of liquid helium the temperature was measured along the axis of a channel carrying a supercritical heat current. A single thermometer on a traversing assembly was used permitting local measurements both in the interior of the channel and in the jet formed in the free fluid. The temperature gradient in the interior of the channel is found to be in agreement with the Gorter-Mellink law up to the lamda point, but goes to zero within a channel diameter, in the free jet. Since the relative velocity between the two fluids is probably continuous along the axis of the jet in the vicinity of the exit, the disappearance of the temperature gradient appears to be inconsistent with the predictions of the Gorter-Mellink term. The Gorter-Mellink A(T) was also measured up to the lamda point. A much stronger divergence is found as Tλ is approached than was indicated by previous measurements.

An experimental investigation of the flow and heat transfer characteristics in internal coolant passages of gas turbine airfoils has been conducted. The PIV method was employed for the flow measurements. A stereoscopic PIV system was used and automated. The stereoscopic method allowed measuring the three velocity components in measurement planes. The system was capable of measuring 100 planes in each configuration. Each measurement plane was composed of 30*30 measurement points. The transient liquid crystal technique was adopted for the heat transfer measurements. Full surface Nusselt number distributions were obtained on all the five outer walls of the test models. The transient TLC technique was adapted in large-scale models of internal cooling channels. The gas temperature evolution in location and time was taken into account in the data processing. CFD simulations have been performed in the measured passage configurations. For the calculations, the unstructured flow solver FLUENT/UNS was employed. A test rig was designed and constructed for the experiments to meet the requirements of the intended investigation. For the present investigation, the test section was a large-scale model of a two-pass coolant passage with a sharp 180° bend. Four different coolant passage configurations were tested: A passage with 45° ribs (baseline configuration). A passage similar to the baseline configuration with extraction holes simulating film-cooling extraction. A passage with film-cooling extraction and a turning vane in the bend region. A passage with ribs 50% bigger than in the baseline configuration. This passage also had a turn region back wall angled at 30° to the incoming flow. The four configurations were tested at three Reynolds numbers (25,000, 50,000, 70,000 based on the hydraulic diameter). The configurations with extraction were tested at three extractions (30%, 40%, 50% of the inlet massflow). For the first time, the PIV and TLC techniques were employed simultaneously for a detailed investigation of the turbulent flow and heat transfer characteristics within internal coolant passages connected with 180° turns. The following conclusions can be drawn: 3D-streamlines were extracted from the flow measurements in the various cooling channels. The streamlines underlined the strong influence of both the ribs and the bend geometry on the creation of the secondary flow motion in the channels. The secondary flow motion dominates the heat transfer in the entire cooling channel. In the fully developed region, the rib-induced vortex governs the heat transfer distribution on the ribbed walls behind the ribs, and also on the sidewalls. In the bend region, the bend corner flow cells (with low streamwise velocity motion) deviate the bend incoming flow. They act as if the sharp bend geometry was modified. This geometry modification is very dependant on the studied configuration. The resulting heat transfer distribution is thus strongly configuration dependant. The regions of high heat transfer in the channels have been linked with high impinging flow regions. High gradients of mean impinging velocity components near the walls induce high heat transfer on the wall. In these regions, the Nusselt number showed a good correlation with the Reynolds normal stress corresponding to the impinging velocity. The configurations with extractions have the best thermal performances at all the tested Reynolds numbers. The variation of the extraction ratio does not modify substantially the thermal performances. CFD tools has benefited from the tremendous progress of computing power. 3D simulations of internal cooling configurations are now possible. CFD predictions have gained accuracy in such highly 3D flow problems. The predictions compared well with the measurements, with worst discrepancies of 25%.

The technology of cooling by boiling has been gaining attention in the fields of hardening of metals, nuclear reactors or superconducting coils. The boiling heat transfer involves not only transportation of sensible heat but also the latent heat due to gas-liquid phase transition, and therefore, it produces high heat transfer rates. The purpose of this on-going study is to elucidate the effects on the cooling by boiling heat transfer when a frost-layer coating is formed on the cooling surface. We are currently experimentally investigating the boiling heat transfer characteristics of copper balls in the diameter range of 20 to 30 mm in saturated liquid nitrogen at atmospheric pressure. The experimental results show that a frost layer coating on the cooling surface has a remarkable effect on the cooling curves of a copper surface.